Question

A trader wants to buy 500 shares of Stock A and decides to hedge the value of her position with futures contracts on Stock B. Each futures contract of Stock B is on 25 shares. Suppose the spot price of Stock A is $5 per share, and the standard deviation of the change in this price over the life of the hedge is estimated to be $0.33. The futures price of Stock B is $4 per shares and the standard deviation of the change in this over the life of the hedge is $0.43. The coefficient of correlation between the spot price change and futures price change is 0.89.

(a) What is the minimum variance hedge ratio?

(b) What position should the trader enter into?

(c) What is the optimal number of futures contracts when issues associated with daily settlement are considered?

Now suppose Stock A is dividend-paying, with $1 dividend paid for each 3 months. The spot price of a Stock A is $5, and the risk-free rate of interest is 8% per annum with continuous compounding.

(d) What are the main differences between forwards and futures?

(e) What are the forward price and the initial value of a one-year forward contract on one share of Stock A?

(f) Four months later, the price of the stock is $6 and the risk-free interest rate is still 8%. What are the forward price and the value of the forward contract?

Answer 1

a) The minimum variance hedge ratio

= correlation coefficient between of standard deviation of change in spot prices and change in futures prices * standard deviation of change in spot prices / standard deviation of change in futures prices

= 0.89* $0.33/$ 0.43

= 0.683

b) The trader should short (Sell) the Futures contract of stock B

c) The optimal no of contracts to be shorted are given by

No of Futures contract of stock B to be sold = hedge ratio * value of stock A/ value of one futures contract of stock B

= 0.683* ($5 *500) / ($4*25)

=17.07

So, the trader should sell 17 Futures contract of B to hedge the position in Stock A